Randall-Sundrum Metric: Causes of Warping

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SUMMARY

The Randall-Sundrum metric, defined as ds^2 = e^{-2ky}g_{ab}dx^adx^b - dy^2, illustrates the warping of spacetime due to the interaction of branes separated by a distance k, as inspired by string theory. This warping occurs similarly to the gravitational effects near massive objects, such as cosmic strings, leading to variations in redshift across different scales. The computation of the exact metric from the field equations is complex but manageable, as the solution is approached through an ansatz. The discussion also touches on the concept of KK excitation, which relates to the energy states of particles in a quantum well.

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  • Understanding of the Randall-Sundrum model
  • Familiarity with string theory concepts
  • Knowledge of spacetime metrics and their implications
  • Basic principles of quantum mechanics, particularly quantum wells
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  • Research the original Randall-Sundrum papers for detailed derivations
  • Explore the implications of KK excitation in higher-dimensional theories
  • Study the effects of cosmic strings on spacetime geometry
  • Learn about ansatz methods in solving field equations in theoretical physics
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The discussion is beneficial for theoretical physicists, cosmologists, and advanced students interested in higher-dimensional theories and the implications of warping in spacetime metrics.

touqra
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The Randall-Sundrum metric for extra dimension is the following:

ds^2 = e^{-2ky}g_{ab}dx^adx^b - dy^2

What is causing this warping or strange metric? I mean a space without force should be totally flat like what we deal with in SR, so there must be something that is causing this warping.
 
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Thats a good question, and you really have to go back to their original papers for the full details (its semi inspired from String theory where say branes separated by a distance k are interacting). But the full computation of the exact metric from the field equations is afaik, fairly involved.

From classical reasoning though, its the same thing as warping in the vicinity of any massive object (eg say a cosmic string), eg the redshift at one end of (picture a compactified cylinder naively) the throat (or Brane) is quite naturally a different scale than the other end, this *warps* spacetime and crumples up that finite dimension, as you can see from that exponential factor in the metric.

(edit: Not that involved actually, because they ansatz the solution... see
http://arxiv.org/PS_cache/hep-ph/pdf/9905/9905221v1.pdf)
 
Last edited:
Haelfix said:
Thats a good question, and you really have to go back to their original papers for the full details (its semi inspired from String theory where say branes separated by a distance k are interacting). But the full computation of the exact metric from the field equations is afaik, fairly involved.

From classical reasoning though, its the same thing as warping in the vicinity of any massive object (eg say a cosmic string), eg the redshift at one end of (picture a compactified cylinder naively) the throat (or Brane) is quite naturally a different scale than the other end, this *warps* spacetime and crumples up that finite dimension, as you can see from that exponential factor in the metric.

(edit: Not that involved actually, because they ansatz the solution... see
http://arxiv.org/PS_cache/hep-ph/pdf/9905/9905221v1.pdf)

In the paper above, there's this term called KK excitation. What does it mean? If it means excitation like the n-excitation states of a particle in a quantum well, then, I don't really understand how it is calculated in this metric...
 

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